run down vs go after

run down and go after both are verbs.

Word	Noun	Adjective	Verb	Adverb
run down	No	No	Yes	No
go after	No	No	Yes	No

As verbs, go after is a hypernym of run down; that is, go after is a word with a broader meaning than run down:

Other hypernyms of run down include chase, chase after, dog, give chase, tag, tail, track, trail.

run down (verb)	go after (verb)
use up all one's strength and energy and stop working	go in search of or hunt for
injure or kill by knocking (someone or something) down and passing over the body, as with a vehicle	go after with the intent to catch
pursue until captured
move downward
examine hastily
deplete
trace